I must say I have a tough time explaining why conceptual fluency is so critical in my eyes.
But I have to defer to the fact that research says that neither conceptual nor procedural fluency is better than the other. That they both are a dynamic duo that serve to make a student flexible with numbers and able to tackle abstract concepts with more than just speed and accuracy. They help as student be flexible in their approach to numbers and concepts/skills.
Let's say I wanted to multiply 7 x 7 but UGH, I don't know my "sevens". But I do know my "fives". So I could decompose 7 into 5 and 2 (as addends) and multiply (or skip count by 5 until I get to 7) seven times 5 to get a partial product of 35. Ooooh and I also know my twos!! So I could skip count by 2 until I get to 14 as another partial product). Well when I combine 35 and 14, I get the same product of 49. Although that abstract understanding will follow; this way I have built a better foundation of understanding behind why I even multiplied 7x7 to find that product rather than a rote "because my teacher said to memorize my fact" or listing out all of my sevens by counting up seven on my fingers and listing each product on the side of my paper! Both take some time, but one approach helps a student in a more scaffolded approach to better grasp their understanding of what 7x7 (or any fact for that matter) is as a final product!
So I stick to my argument that conceptual focus BEFORE procedural focus, builds a better equipped WHOLE student.
Think about these two concepts approached in 4th and 5th grade respectively. What happens when students begin to multiply larger whole numbers and eventually decimal numbers? They already have an understanding of decomposing numbers as well as using partial products to support this approach. This is all about decomposition...which builds from a conceptual understanding of numbers!
So, for my 3rd grade teachers who serve our babies on the front lines of fact fluency.
Here's a video series for you, that encompasses teacher and student stations for your classroom. All around facts (multiplication) from a conceptual standpoint! Before a baby ever gets on a computer to play a fact game, this helps build their foundation of numbers so their fluency truly is procedural in that they can manipulate numbers rather than "rotely" spew out facts with speed!
I would encourage pre-assessing your student with a running record to see what strategies they might already know. Click here
